TSTP Solution File: SEV168^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV168^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 18:05:11 EDT 2022
% Result : Theorem 1.97s 2.16s
% Output : Proof 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 46
% Syntax : Number of formulae : 51 ( 9 unt; 4 typ; 1 def)
% Number of atoms : 99 ( 29 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 167 ( 27 ~; 21 |; 0 &; 85 @)
% ( 20 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 22 con; 0-2 aty)
% Number of variables : 72 ( 57 ^ 15 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_p,type,
p: ( a > a > a ) > a ).
thf(ty_q,type,
q: ( a > a > a ) > a ).
thf(ty_eigen__0,type,
eigen__0: a > a > a ).
thf(h0,assumption,
! [X1: ( a > a > a ) > $o,X2: a > a > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: a > a > a] :
( ( p @ X1 )
!= ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ( q
= ( ^ [X1: a > a > a] :
( X1
@ ( q
@ ^ [X2: a,X3: a] : X2 )
@ ( q
@ ^ [X2: a,X3: a] : X3 ) ) ) )
=> ( p
!= ( ^ [X1: a > a > a] :
( X1
@ ( q
@ ^ [X2: a,X3: a] : X2 )
@ ( q
@ ^ [X2: a,X3: a] : X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( p @ eigen__0 )
!= ( q @ eigen__0 ) )
=> ! [X1: a] :
( ( ( p @ eigen__0 )
= X1 )
=> ( X1
!= ( q @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > a > a] :
( ( q @ X1 )
= ( X1
@ ( q
@ ^ [X2: a,X3: a] : X2 )
@ ( q
@ ^ [X2: a,X3: a] : X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > a > a] :
( ( p @ X1 )
= ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( q @ eigen__0 )
= ( eigen__0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) )
=> ( ( eigen__0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) )
= ( q @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( ( p @ eigen__0 )
= X1 )
=> ( X1
!= ( q @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ( p @ eigen__0 )
= ( eigen__0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) )
=> ( ( eigen__0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) )
!= ( q @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( q @ eigen__0 )
= ( eigen__0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( p
= ( ^ [X1: a > a > a] :
( X1
@ ( q
@ ^ [X2: a,X3: a] : X2 )
@ ( q
@ ^ [X2: a,X3: a] : X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a,X2: a] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( p @ eigen__0 )
= ( q @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( p @ eigen__0 )
= ( eigen__0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > a > a] :
( ( p @ X1 )
= ( X1
@ ( q
@ ^ [X2: a,X3: a] : X2 )
@ ( q
@ ^ [X2: a,X3: a] : X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ( ( q @ eigen__0 )
= X1 )
=> ( X1
= ( q @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( p = q ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP1
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a,X2: a > $o] :
( ( X2 @ X1 )
=> ! [X3: a] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a > $o] :
( ( X1 @ ( p @ eigen__0 ) )
=> ! [X2: a] :
( ( ( p @ eigen__0 )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) )
= ( q @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( q
= ( ^ [X1: a > a > a] :
( X1
@ ( q
@ ^ [X2: a,X3: a] : X2 )
@ ( q
@ ^ [X2: a,X3: a] : X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cTHM188_PARTIAL_pme,conjecture,
sP16 ).
thf(h1,negated_conjecture,
~ sP16,
inference(assume_negation,[status(cth)],[cTHM188_PARTIAL_pme]) ).
thf(1,plain,
( ~ sP3
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP20
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP8
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP14
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| ~ sP12
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP2
| sP11
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP18
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP17
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
sP17,
inference(eq_ind,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP1
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP1
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP10
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
sP10,
inference(eq_sym,[status(thm)],]) ).
thf(17,plain,
( sP4
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(18,plain,
( sP15
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP16
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP16
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h1]) ).
thf(22,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[21,h0]) ).
thf(0,theorem,
sP16,
inference(contra,[status(thm),contra(discharge,[h1])],[21,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEV168^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 14:45:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.97/2.16 % SZS status Theorem
% 1.97/2.16 % Mode: mode506
% 1.97/2.16 % Inferences: 14
% 1.97/2.16 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------